Listen to Robert Emmerich introduce The Big Apple, a hit song from 1937. Music written by Bob and performed by Tommy Dorsey's Clambake Seven with Bob on piano. Lyrics written by Buddy Bernier and sung by Edythe Wright. Audio provided by Dorothy Emmerich.

"Okey-dokey” or “okie-dokie’ (an extension of “O.K.") has been in use since the 1930s. “Okey-dokey, artichokey” (also “Okie-dokie, artichokie") has been cited in print since at least 1988. Hillary Rodham Clinton—then first lady—made the term famous in the 1990s when she ended staff meetings with this folksy phrase.

“Okey-dokey, artichokey” has appeared in articles about artichokes, but the rhyming alone is responsible for “artichoke” being in the phrase. Another popular ending is “Okey-dokey, smokey.”

Urban DictionaryOkey Dokey Artichokey
A derivation of goodbye. Usually used after, “See you later alligator!”
CAUTION: Do not use with great frequency, for fear of looking like a big idiot.
X: I’m going to get the hell outta here.
Y: Okey dokey artichokey!
X: WHAT?
by Suave, Rico Dec 2, 2004

Wikipedia: Artichoke
The Globe Artichoke (Cynara cardunculus) is a perennial thistle originating in southern Europe around the Mediterranean. It grows to 1.5-2 m tall, with arching, deeply lobed, silvery glaucous-green leaves 50–80 cm long. The flowers develop in a large head from an edible bud about 8–15 cm diameter with numerous triangular scales; the individual florets are purple. The edible portion of the buds consists primarily of the fleshy lower portions of the involucral bracts and the base, known as the “heart”; the mass of immature florets in the center of the bud is called the “choke”. These are inedible in older larger flowers.

B. adj. = OK adj. 1.
1936 N.Y. Times 25 June 23/5 He suffered no pain. He pranced around the deck occasionally, announcing that he was ‘okey dokey’.
1968 F. EXLEY Fan’s Notes (1970) v. 213 His secretary..informed me that her boss was a ‘genius’ and never offered explanations other than ‘This is terrible’ or ‘This is okie-dokie’.
1977 J. FLEMING Every Inch Lady I. i. 7 Light out, silence, everything okey dokey, she goes off to bed.

Google BooksBecoming Teachers:
Preservice Teachers’ Understanding of School and Society
By David William Hursh
Published by University of Wisconsin--Madison
1988
Pg. 124:
He playfully closed one conversation with a student with “Okie, dokie, artichokie.”

i’m going home today for easter, so could you email any replies & while i’m home i’ll work out on paper what i’ve worked out of the following songs, & send it when i come back, okey dokey artichokey

New York (NY) TimesLiberties; Letters From the Edge
By MAUREEN DOWD
Published: January 25, 1996
Jealous of the attention the special prosecutor is getting by subpoenaing Hillary Rodham Clinton to testify before a Federal grand jury, Al D’Amato tries to grab back the spotlight by accepting Mrs. Clinton’s offer to answer questions from the Whitewater Committee in writing.
(...)
Q. Carolyn Huber, your friend and Chelsea’s trusted baby sitter, told the committee that she hasn’t spoken with you since Dec. 23. Not even a word on Christmas. This sudden silence disturbs me. Well?

A. Okey dokey, artichokey. The White House pastry chef gave me the secret to perfect S’Mores: You melt the Hershey bar a little before you put it on the marshmallows and graham crackers. Mmm, good. Bill loves them. He eats three at a time. Oh, and he says they’re great with tomato sauce!

Newsweek magaine (November 18, 1996)Masters Of Disaster
The Scent Of Scandal: How The White House Shored Up Its Defenses Against A Sea Of Troubles And Managed To Blunt The Gop Candidate’s Re-Emergence As Citizen Dole
(...)
The steadfastness of Hillary’s staff was remarkable. “"Hillaryland,’’ the suite of offices occupied by the First Lady’s staff in the Old Executive Office Building, was about the only part of the White House that did not leak. Mrs. Clinton was able to command great affection and loyalty by playing the role of den mother to her mostly young assistants. She could be silly, wearing a Christmas necklace of flashing lights; or corny, exclaiming, “"Okey-dokey, artichokey,’’ or sometimes a little prudish, admonishing some of the women on her staff for wearing too short skirts.

The first time I heard the phrase okie-dokie-artichokie was around 1982, spoken by a younger person that I’d recently hired. I assumed the person had picked up the phrase from the pop culture at the time.